Brownian Dynamics Simulation of the Capture of Primary Radicals in Dispersions of Colloidal Polymer Particles

Abstract

The kinetics of collision between primary persulfate radicals and colloidal polymer particles, a key issue in emulsion polymerization modeling, is determined by the simulation of Brownian dynamics using a Monte Carlo random flight algorithm. The results obtained confirm the ideal behavior predicted by Smoluchowski's kinetic equation only in colloidal dispersions of very low polymer volume fractions (<0.1%), while at higher values, significant deviations from ideality are observed. This deviation from ideality, designated as the Smoluchowski number (Sm), is found to increase almost linearly with the volume fraction of the dispersion. The kinetic model considering the effect of volume fraction is compared with previous experimental data. A satisfactory explanation for the different functional dependences of the radical entry rate on particle diameter is obtained. It is concluded that the polymer volume fraction in the dispersion plays a major role in the mechanism of radical capture by polymer particles.

Brownian Dynamics Simulation Studies on Radical Capture in Emulsion Polymerization

“…[9] The rates of radical capture obtained from the Brownian Dynamics simulations of dilute dispersions (volume fractions below 0.1%) in the absence of interaction potentials and in the absence of energy barriers for radical capture, were in very good agreement with the values predicted using the analytical solution derived by Smoluchowski [10] (Equation 1). On the other hand, a significant effect of volume fraction on radical capture rates was observed in systems above 0.1% volume fraction, where most polymer dispersions with any practical interest are found.…”

Radical Desorption Kinetics in Emulsion Polymerization, 2 – Brownian Dynamics Simulation of Radical Desorption in Non‐Homogeneous Particles

“…In this case, when the diffusion coefficient in the core is small compared to the diffusion coefficient in the shell, the fitted parameters correspond to the values obtained using Equation (6), and therefore, the simple desorption rate coefficient can be estimated using the volume fraction averaged diffusion coefficient presented in Equation (5)…”

“…where j is a random number obtained from a Gaussian distribution with mean zero and variance 1, D p the diffusion coefficient of the radical inside the particle, and dt is the variable time-step which is constantly updated to reduce computation time, according to Equation (3): [6] dt…”

“…[6] By means of Equation (2), the error involved in the estimation of the desorption time is minimized by increasing the time resolution of the simulation as the radical approaches the surface of the particle. The time resolution limit is determined by the relaxation time of the diffusing radical.…”

Adaption of the Mechanism of Emulsion Polymerization to New Experimental Results

“…[28] These numerical experiments allow effective simulation of a variety of experimental conditions regarding the size and the concentration of the particles. Note, models relying on the Smoluchowski equation are insufficient as it is valid for a single particle at infinite dilution.…”